Question

Consider the following scenario:

• Let P(C) = 0.4
• Let P(D) = 0.5
• Let P(C | D) = 0.6

1.) Find P(C AND D).

2.) Are C and D mutually exclusive? Why or why not? select a letter for your answer

(A.) C and D are not mutually exclusive because P(C) + P(D) ≠ 1

(B.) C and D are mutually exclusive because they have different probabilities.

(C.) C and D are not mutually exclusive because P(C AND D) ≠ 0

(D.) There is not enough information to determine if C and D are mutually exclusive.

3.) Are C and D independent events? Why or why not? Select a letter for your answer

(A.) The events are not independent because P(C | D) ≠ P(C)

(B.)The events are independent because they are mutually exclusive.

(C.) The events are not independent because the sum of the events is less than 1.

(D.) The events are not independent because P(C) × P(D) ≠ P(C | D)

4.) Find P(D | C).

Answer 1

Answer:

1. P(C AND D) = 0.3

2. (C.) C and D are not mutually exclusive because P(C AND D) ≠ 0

3. (A.) The events are not independent because P(C | D) ≠ P(C)

4.P(D | C) = 0.5

Step-by-step explanation:

• Let P(C) = 0.4

• Let P(D) = 0.5

• Let P(C | D) = 0.6

1.) Find P(C AND D).

$P(C | D) = \frac{P(C n D)}{P(D)} \\P(C n D) = P(C | D) * P(D)\\P(C n D) = 0.6 * 0.5\\P(C n D) = 0.3$

2.) Events can be mutually exclusive meaning the both event cannot happen at the same time. So, P(A and B) = 0

3.) Events can be "Independent", meaning each event is not affected by any other events.

4.) Find P(D | C)

$P(D | C) = \frac{P (D n C)}{P(C)}\\P(D n C) = 0.5 * 0.4 = 0.2\\P(D | C) = \frac{0.2}{0.4}\\P(D | C) = 0.5$